Infinite-dimensional Luenberger-like observers for a rotating body-beam system

Systems and Control Letters

Volumn 60, Issue 2, 2011, Pages 138-145

  Li, Xiao Dong ^a   Xu, Cheng Zhong ^b,c  

^a INRIA   (France)

^b UNIVERSITÉ LYON 1   (France)

^c UNIVERSITÉ LYON 1   (France)

Author keywords

Euler beam equation; Exact observability; Exponential convergence; Finite element method; Observers; Partial differential equations

Indexed keywords

NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; ROTATING MACHINERY;

DYNAMIC EVOLUTION; EULER BEAM; EXACT OBSERVABILITY; EXPONENTIAL CONVERGENCE; INFINITE DIMENSIONAL; OBSERVATION SYSTEMS; OBSERVERS; ROTATING BODY-BEAM;

FINITE ELEMENT METHOD;

EID: 79251599145     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2010.11.005     Document Type: Article

References (26)

1. J.M. Coron, and B. d'Andrea-Novel Stabilization of a rotating body-beam without damping IEEE Transactions on Automatic Control 43 1998 608 618
2. J.P. Gauthier, and I. Kupka A separation principle for bilinear systems with dissipative drifts IEEE Transactions on Automatic Control 37 1992 1970 1974
3. F. Celle, J.P. Gauthier, D. Kazakos, and G. Sallet Synthesis of nonlinear observers: a harmonic analysis approach Mathematical Systems Theory 22 1989 291 322
4. C.Z. Xu, P. Ligarius, and J.P. Gauthier An observer for infinite-dimensional dissipative bilinear systems Computers & Mathematics with Applications 29 1995 13 21
5. J.P. Gauthier, C.Z. Xu, and A. Bounabat An observer for infinite-dimensional skew-adjoint bilinear systems Journal of Mathematical Systems, Estimation, and Control 8 1998 31 50
6. M. Demetriou Natural second-order observers for second-order distributed parameter systems Systems & Control Letters 51 2004 225 234
7. M. Demetriou, and F. Fahroo Model reference adaptative control of structurally perturbed second-order distributed parameter systems International Journal of Robust and Nonlinear Control 16 2006 773 799
8. T.D. Nguyen, and O. Egeland Infinite dimensional observer for a flexible robot arm with a tip load Asian Journal of Control 10 2008 456 461
9. T.D. Nguyen, O. Egeland, Observer design for a towed seismic cable, in: The Proceeding of the 2004 American Control Conference, Boston, Massachusetts, 2004, pp. 22332238.
10. G. Weiss, R.F. Curtain, Exponential stabilization of vibrating systems by collocated feedback, in: Proceedings of the 7th IEEE Mediterranean Symposium on Control and Automation, Haifa, Israel, 1999.
11. V. Jurdjevic, and J.P. Quinn Controllability and stability Journal of Differential Equations 28 1978 381 389
12. A.J. Deguenon, G. Sallet, C.Z. Xu, A Kalman observer for infinite dimensional skew-symmetric systems with application to an elastic beam, in: Proceedings of the Second International Symposium on Communications, Control and Signal Processing, Marrakech, Morrocco, 2006.
13. J. Bailleuil, and M. Levi Rotational elastic dynamics Physica D 27 1987 43 62
14. A.M. Bloch, and E.S. Titi On the dynamics of rotating elastic beams Conte Perdon Wyman Proc. Conf. New Trends System Theory 1990 Birkhuser Genova, Italy
15. C.Z. Xu, and J. Baillieul Stabilizability and stabilization of a rotating body beam system with torque control IEEE Transactions on Automatic Control 38 1993 1754 1765
16. C.Z. Xu, and G. Sallet Boundary stabilization of rotating flexible system Curtain Bensoussan Lions Lectures Notes in Control and Information Sciences vol. 185 1992 Springer-Verlag New York 347 365
17. O. Morgul Control of a rotating flexible structure IEEE Transactions on Automatic Control 39 1994 351 356
18. A. Pazy Semigroups of Linear Operators and Applications to Partial Differential Equations 1983 Springer-Verlag New York
19. M. Tucsnak, and G. Weiss Simultaneous exact controllability and some applications SIAM Journal on Control and Optimization 38 2000 1408 1427
20. M. Tucsnak, and G. Weiss Observation and Control for Operator Semigroups Birkhuser Advanced Texts 2009 Birkhuser Basel
21. N. Cndea, S. Micu, M. Tucsnak, An approximation method for exact controls of vibrating systems, Manuscript (2010) (17 pages) (submitted for publication).
22. B.Z. Guo, and Z.C. Shao Regularity of a Schrodinger equation with Dirichlet control and colocated observation Systems & Control Letters 54 2005 1135 1142
23. B.Z. Guo, and X. Zhang The regularity of the wave equation with partial Dirichlet control and collocated observation SIAM Journal on Control and Optimization 44 2005 1598 1613
24. I. Lasiecka, and R. Triggiani L 2 (Σ ) -regularity of the boundary to boundary operator B * L for hyperbolic and Petrowski PDEs Abstract and Applied Analysis 19 2003 1061 1139
25. X.D. Li, C.Z. Xu, Y.J. Peng, M. Tucsnak, On the numerical investigation of a Luenberger type observer for infinite-dimensional vibrating systems, in: Proceedings of the 17th IFAC World Congress, Seoul, Korea, 2008.
26. B.P. Rao Le taux optimal de dcroissance de l'nergie dans l'quation de poutre de Rayleigh Comptes Rendus de l'Acadmie. des Sciences, Series I - Mathematics 325 1997 737 742